texts: To show perihelion precession motion of Mercury in Python with matplotlib

texts:
I'm trying to make it more general code so I can trace even a parabola or hyperbola for $e=1, E=0$ and $e>1, E>0$ respectively. And after achieving that general code I want to make the same code working for perihelion precession motion of Mercury just by adding an additional term ($-A/r^3$) in the energy term. Feel free to change my entire code and energy term.

from numpy import *
import matplotlib.pyplot as plt

L = 9.11*10**38     #L = angular momentum
m = 3.28*10**23     #m = mass of mercury
M = 1.99*10**30     #M = mass of sun
a = 5.8*10**10       #a = semi-major axis
G = 6.674*10**-11   #G = Gravitationl constant
k = G*M*m
E = -k/(2*a)        #E = energy
##E = 0
p = L**2/(m*k)
c = 1 + (2*E*L**2)/(m*k**2)
e = sqrt(c)       #e = eccentricity
print(e,c)
def fx(x):
    r = p/(1 + e*cos(x))
    return float(r)

n = 1000
phi =linspace(0,2*pi,n)
radius = zeros([n])
theta = zeros([n])
x = zeros([n])
y = zeros([n])

for i in range(0,n):
    radius[i] = fx(phi[i])
    theta[i] = 180*phi[i]/pi

for i in range(0,n):
    x[i] = radius[i]*cos(phi[i])

for i in range(0,n):
    y[i] = radius[i]*sin(phi[i])

print('r =',radius)
print('x =',x)
print('y =',y)
plt.plot(x,y)
plt.show()


texts:
For the last week or so, I have been teaching myself orbital mechanics within the context of Braeunig's Rocket and Space Technology.

I noticed a symbol, $\phi '$, and was wondering what context that was used in? I think it is an angle measurement, but I know that it is almost equal to the semi-major axis on earth.

From the box labeled Geodetic Latitude, Geocentric Latitude, and Declination, found about half way down after selecting Orbital Mechanics here.


texts: C-Type Asteroids and Carbonaceous Chondrite Meteorites

texts: I was just wondering, what is the relationship between C-type asteroids and carbonaceous chondrite (CC) meteorites? Do CC meteorites come from C-type asteroids?


texts: When exactly does a sub giant become a red giant?

texts:
A simple, but interesting question I think.
I understand that after the hydrogen exhaustion on the main sequence the post main sequence starts with the SGB where they burn hydrogen in a shell around the Helium core.
We also know that stars under $ 2 M_{\odot }$ experience a Helium flash and start Helium core fusion after the Red giant tip. Whereas stars greater than $2 M_{\odot }$ do not experience this Helium flash and starting the He-core burning immediately after the SGB without a helium flash (very massive stars burn Helium on the main sequence).

My question is now what specific physical process happens in a sub giant, which makes it a red giant afterwards?

Thank you in advance (I am very open for mathematical/physics explanations as well, since I study physics myself).


texts: Is the moon's orbit circularizing? Why does tidal heating circularize orbits?

texts: The moon has an elliptical orbit (of course), but as it inches away from the Earth each year, does its orbit become more circular and how come? Io's orbit is becoming more circular due to tidal heating effects, but why?


texts:
What is the definition of a "pole" of a celestial body?
Earth's pole is defined as it's rotational pole.  The North and South Poles are the two points on Earth where its axis of rotation intersects its surface.
Apparently, (according to everywhere I've read), the poles of astronomical bodies are determined based on their axis of rotation in relation to the celestial poles of the celestial sphere.  But this is an inadequate definition.
What about Pluto?  Pluto's axis of rotation does not intersect its surface.  Pluto is tidally locked with Charon, and Pluto orbits a barycenter that is located outside of Pluto.  And yet Pluto has a North and a South Pole.  Why are the North and South Poles of Pluto where they are, as opposed to any other location on the surface of Pluto?
How are these poles defined for Pluto?
What is the definition of a "pole" of a celestial body?


texts: Formation of a magnetosphere for gas giants / small stars

texts:
This question got me thinking about this.

Jupiter has, and presumably super-Jupiters can have a strong magnetospheres.  A solid metallic core and rotating material around the core, creates a magnetic field and all 4 gas planets in our solar-system have magnetic fields, though Jupiter's is by far the strongest.   Source

As I understand it, a planetary magnetic field requires a solid core and a slight variation in rotation where the liquid outer core rotates in relation to the solid inner core.  The planet's speed of rotation might not be necessary, but it could be a factor.

During the hot period of formation, gas giants might not form magnetic fields but when they cool down enough to have a solid core, they probably would have them.

So, the question is, is there a rough mass for which planet-wide magnetic field formation becomes unstable, where the core of the heavy Jupiter or small or old brown dwarf takes a very very long time to solidify, say, many billions of years?

I'd think the high temperature of formation and additional heat from fusion in a Brown Dwarf wouldn't be a good situation for that kind of star-wide magnetic field to form due too inevitable convection and probably no solid core.   That kind of star would probably form multiple magnetic dipoles like our sun has, but perhaps in an older brown dwarf a single magnetic field might be possible.

White dwarfs have very strong magnetic fields, so pressure obviously isn't an issue, in fact, I think high pressure can create a stronger magnetic field.


texts: gravitational energy and internal energy

texts:
So assume we have a planet of temperature T, and mass M, We can calculate it's internal energy/heat content by the formula $U=cMT$ where $c$ is the specific heat.

And if we also know the gravitational energy of the planet via $\frac{GM^2}{R}$

how do I approach the following question?

Can the release of gravitational energy during planet formation in principle (is there enough) explain this much heat

Any help would be appreciated.


texts: What's the map on Sheldon & Leonard's refrigerator of?

texts: In the Big Bang Theory, there's a map on Sheldon & Leonard's refrigerator throughout the entire show It has false-color shadings of various kinds, with prominent craters, and so is presumably of some non-terrestrial body, perhaps Mars, the moon, or an asteroid. Can anyone identify it?


texts: Do comet tails increase as comets move away from the Sun?

texts: Do the tails of comets increase on their return trip from the Sun?


texts: How much of a molecular cloud can end up as "starstuff"?

texts:
Stars form within molecular clouds. These clouds can be up to 6 millions solar masses. When the cloud collapses into stars, is it possible to know a rough figure for how much of this material actually turns into stars? 1%? 99%?

Do larger clouds tend to be more mass-efficient in star formation than smaller ones?


texts: Different times of sunset at the same location due to elevation

texts:
Me and my friend were watching the sunset on the same location (at my country the latitude is approximately 40 degrees). I am at sea level and my friend is at an elevation. He observed the sunset with a difference of about 4 minutes than me. He is a physicist so he challenged me to find out his elevation. Any ideas on how to use these information and win the challenge?
I found some information on Wikipedia here but cannot understand a lot.
Any idea on how to solve this will be appreciated. Thanks in advance for your help.


texts: Statistics of elements abundance in exoplanets

texts:
Recently, I encountered the concept of carbon planets - planets, which would be, unlike the Earth, formed mostly by carbon, instead of oxygen, silicon and magnesium. (I am not counting iron, which is mostly locked in the core). Now, I am interested in the planetary chemical compositions in general. I found interesting articles investigating the topic of variance of the planetary chemical compositions (for example here or here), but it is quite hard for me to make an overall picture of the state in the field.

I would like to ask on these things:

1. What typical compositions of terrestrial planets are expected to occur? (I guess there will be plenty of correlations, some groups of elements occuring together as they are bound, for example to the CNO cycle or other nuclear cycle.)

2. How much different the chemical compositions of terrestrial planets really are? (I.e. are all terrestrial planets mostly similar to each other, or should one rather expect that every planetary system has unique ratios of elements?)


texts: Source for Identification of Balmer Hydrogen Absorption Lines

texts:
I'm working on an assignment, where I have to classify stars using the raw data of the telescope. I'm now trying to calibrate the pixel to armstrong ratio, and for that I need to identify the absorption lines present on the star.

I've been researching for two days now, and I haven't been able to find a 'trustworthy' source of information/confirmation on where to set the Balmer absorption lines for a star like the one in the image (I'm positive H alpha (the one at the far right), beta (on top) and gamma (i would say the one at the left of H beta) are quite prominent).

So far, I am trusting on this page to do it. Is there a real source of info, be it a book, an institutional webpage or something, where I can confirm and that I could reference for an assignment? Am I wrong on the position of the Balmer Series?


texts: Maximum and minimum gas giant & ice giant densities

texts:
I'm working on a star system generator for a game; I'd like its results to be plausible but they needn't be super-realistic. I've got the orbital distances and masses of each body in the system, and now want to render them, so I need to determine the radius of each body.

For gas giant and ice giant planets, what's the relationship between mass and density? What are the minimum and maximum densities expected?


texts: Can the diminishing energy of the CMBR be the source of dark energy?

texts: I was just told the CMBR energy diminishes with time. Can it be that the lost energy is somehow transferred to spacetime, causing the expansion to accelerate?


texts: What is a singularity (black holes)?  What happens to time and space at that point? What does it leads to?


texts: Will Earth lose the Moon before the Sun goes into supernova?

texts:
Ive read on some sites and saw on youtube videos that the moon is getting away from earth by 1-3 cm a year.

Is this enough to make the Earth lose the Moon before the Sun goes into Supernova?

Im asking because I would like to do the calculations for Earths magnetic pull on this subject. It appears to me that it should be a non-linear function (there are also other factors, like if the Moon could be captured by another planet or having asteroids messing with its orbit on Earth).

Thank you.


texts:
as I was browsing Nasa's Eyes few days ago, I saved a screenshot,  but it seems text is blurrry, supher-485, first letter is S ends with er-485 from as I can read
it kinda looked like Cosmic Web, Indra's net, so i saved cool screenshot
Help me identify this cluster?


texts: Fate of a planet orbiting a Lagrange point behind a star?

texts:
Let's say there is a planet orbiting at L5 behind a star, which is in turn orbiting a more massive star, like so:

What is the ultimate fate of this planet? I'm predicting that it will spiral into the star, or end up in some sort of horseshoe orbit. Is this prediction right? If so, why? If not, where did I go wrong?


texts: What is the role of the random catalogue in calculating the two-point correlation function?

texts:
To study clustering of galaxies and clusters, one makes use of
the two-point correlation function. However, we can see that all
the estimators of $\xi(r)$ use a random catalogue.

What is the random catalogue used for?


texts: How was the axial tilt of planets measured?

texts:
https://en.wikipedia.org/wiki/Axial_tilt#Solar_System_bodies gives the axial tilt of all planets with two decimal precision, but how and when were they measured so precisely ?
I guess it's "easy" for Mars, Jupiter and Saturn (thanks to the rings ?) but how was it measured for Venus under its clouds, or Uranus + Neptune that are so far away ?
Links to scientific publications would be appreciated.
Thanks


texts: Implementation of formulae for Meeus for the Moon

texts:
With Astronomical Algorithms by J. Meeus (1998)
I have obtained the relevant illuminated fraction of the disk and position angle.

But they're numbers (all Greek to me!) I know, Meeus explains that they're ratios of the lengths of the illuminated limb and areas.

Okay, so I have a ratio.  How do I implement that together with the position angle to work out the direction of the illuminated limb and the amount illuminated?

I'm assuming that the ratio 1.0 is totally illuminated (i.e. Full Moon)
and 0.0 is nothing (i.e. New Moon).

and then there is the position angle, I'm assuming that the direction in degrees is starting at 0 pointing upwards.  Is that the crescent shape direction i.e. the horns are pointing away from the directional angle?

I would like to be able plot this so that I can show visually the moon's illuminated fraction and direction for any day in any given year.

As I said, I have the numbers, I'm trying to translate that into a more visually appealling and meaningful result.

Meeus says this is the selenocentric elongation of the Earth from the Sun (Phase Angle) - i.

the formula for illuminated fraction k is:

k = ( 1 + cos i ) / 2

tan i = (R sin l) / (D - (R cos l))

R = distance Earth-Sun
D = distance Earth-Moon
l = geocentric elongation

Meeus calls k the ratio of the lengths BC:AC
the same as the ratio of the areas: NBSC:NASC

Where


texts: There are a lot of objects of different sizes in the Kuiper belt. Are objects in the Kuiper belt stable? Is there any chance in the future that one of the larger objects would accumulate enough critical mass to start the process of becoming a proper planet (i.e., clearing its neighboorhood)?


texts: I'm wondering that what would be the escape velocity of our Galaxy?


texts: Is there a more modern/updated paper than Hurley's 2000 SSE?

texts:
I've implemented equations from Hurley's 2000 paper on Single Stellar Evolution (SSE) to model the stages of stellar evolution without having to use the full SSE code (or MESA for that matter).

Is there a more updated version of such a paper, where numerical formulae are given to model stages of stellar evolution? Has the knowledge base of the field of stellar evolution changed enough in the last 18 years to warrant an updated numerical formula recipe?

Here's the arxiv of the paper.


texts: Finding Latitude and Longitude of a person or of where a picture was taken

texts:
this is my first post on the Astronomy stack exchange site. Please let me know how this question is based on y'all's generally accepted criteria for a good question as well as possible improvements.

In my AP comp sci class we were given pretty much total freedom to come up with a project, I remembered hearing about it being possible to calculate a person's position or the position a picture was taken based on time of day and the position of the Sun, that is, longitudinal and latitudinal position. For the picture, I heard Sun position was determined through some implementation of shadows in the picture. I thought this was cool and decided to look into it. I found an article written by a prominent UCLA physicist and a well-researched Wikipedia page. I understand what the Wikipedia page requires in regards to values for calculations and what the equations calculate, but I do not understand how to implement them to find longitudinal and latitudinal location, nor do I understand why it has rectangular equatorial coordinates as that is not included in the three-step explanation in the Wikipedia page intro at the top.

For the UCLA report, I understand none of it except for the matrix mathematics and manipulations, and I'm sketchy on those at best, but I do not understand all the coordinate systems that it mentions nor how to implement them to achieve my objective.

So my question comes down to this: Can anyone clarify the equations, their purpose, their implementation, how to convert an answer to longitude and latitude for either the Wikipedia page or the UCLA report?

OR

If you can explain how to find the latitude and longitude of a picture or person. If you choose to explain, I do need equations or an explanation that I can turn into equations.

Please suggest question revisions and whether this should be posted on a different Stackexchange forum. Thanks.


texts: Is the Cosmos a super set of the Universe and any hypothetical multiverse(s)?

texts:
I'm quite lost on the definitions of words like omniverse, megaverse, multiverse, meta-universe, universe, and cosmos. I used to think the Universe and the Cosmos were essentially the same things, but now I'm reading the latter is an orderly system (not sure what's meant by that).

Can somebody help me understand what they each represent? In 1980, Carl Sagan said "The cosmos is all that is, or ever was, or ever will be." This sounds like the Cosmos would be the greatest of all and all else would fall into that. Would it be accurate, for example, to say Cosmos > Multiverse > Universe? What about the other things I mentioned earlier?


texts: Is there an element of chance/chaos in stellar evolution?

texts:
Since stars are an ideal example of macroscopic objects, is their evolution  determined by their initial mass and metallicity?

Are there any non-trivial random internal processes going on that may significantly affect a star's development and eventual fate? (It is quite evident that capture of another star or a brown dwarf is an external, exogenous event.)

EDIT/clarification: I'm looking for things that may shorten/extend the lifetime of a star beyond the "norm" prescribed by nuclear physics/gravity, change its composition, surface temperature. Solar flares/quakes and other instabilities come to mind first.


texts: Is there a term for stars without any planets?

texts:
Quite simply, is there any used term for stars that don't have any planets? While contemplating this and doing numerous searches to no avail, I think I found my own answer, but I'm asking here for more input.

The reason I think there is no real term used as such is because there is yet to be confirmed of any stars that do not consist of any planets. I'm aware that we know of stars at this point in time where we haven't identified any planets YET, but that is not the same as actually confirming if planets do or do not exist around the star.

Am I correct in assuming this is the reason why no term has came to fruition yet? Or is there a term used in relation to talking about the possibility of none existing?

I've searched a fair bit for this but haven't been able to find anything. I know that current models show that it's highly unlikely for this to occur, but I'm curious.


texts: Is it Possible for Planetary Bodies To Exist In Close Proximity Without Adverse Effects?

texts:
There are several sci-fi movies where planetary bodies are shown in the sky in order to indicate that the characters are on an alien planet. A good example is in Predators (2010):

Is it actually possible for such planetary bodies to exist so close to each other as to be visible in such detail to the naked eye? Wouldn't gravitational forces cause disruptions on them that inhibit the development of life (whether plant or animal)? In our Solar system there's a good example in Io which has severe volcanic activity resulting from tidal heating due to its proximity to Jupiter.


texts: "Early" and "late" nomenclature regarding O, B & K, M stars

texts:
The Wikipedia article Stellar Classification has a subsection "Early" and "late" nomenclature.
It says:

Stars are often referred to as early or late types. "Early" is a
synonym for hotter, while "late" is a synonym for cooler.

My lecture notes say:

O and B stars are sometimes referred to as ‘early-type’, while K and M
are ‘late-type’.

If I look at a HR diagram, I see that main sequence O, B stars are hotter than main sequence K, M stars. So they are burning their fuel at a greater rate than K, M stars, so they run out of it early. So the stars which we are still able to observe now from the early universe are K, M stars, rather than O, B, which presumably formed rather *late**ly. Yet this is not consistent with the terminology above, so something is obviously wrong here.
What is wrong with my argument that the early and late words should be used in the other way round?


texts: Distance of extra-galactic Classical Cepheids

texts:
There have been many questions and answers about finding the distance of a star from the earth. But as I did some research on the net, I found that we have specific approaches for finding the distances of different types of stars.

So, my question is more specific now.

How to determine how far a Classical Cepheid is?

What if the Cepheid is extra-galactic? Is there a good method to finding the solution?
Can anybody suggest how to make a start at deriving a relation at finding the distance of a Cepheid from us?

There is this Period-Luminosity-Color relation. Can anyone at least enlist the journal articles where I can make a study to get closer to finding the answer to my question?


texts:
What is the red in this picture of earth?  At first we thought it might be pollution, but Jupiter also has red.
Picture source:  https://education.seattlepi.com/primary-movements-motions-earth-4701.html


texts: What would happen to the atmosphere of a rogue jovian planet?

texts:
Let's say we have a gas giant composed primarily of hydrogen and hydrogen-rich molecules that is ejected from its star system.

As this planet embarks on its potentially infinite journey out into the cold darkness of space, away from the light and warmth of its host star, what would happen to its atmosphere? Would the gasses freeze and fall, piling up as winds cease? Would mass be lost? Or would the planet just remain in a relatively similar state? I know Jupiter radiates more heat than it receives from the Sun.


texts: What exactly is a Right Ascension clock and how was one (mounted on a telescope) used in practice, historically?

texts:
@MikeG's answer to Why does this Lowell Observatory telescope have so many knobs? What do they all do? explains that item #6 labeled in the image there (and cropped version here) is likely to be a "Right Ascension clock".

My question is not specifically about the item in the photo, but instead is more general.

If you are operating a large research telescope in the past, when things are all done manually (clock drives, pen and paper), and there was such an object on your telescope, how would you answer the following?

Question: What exactly is a Right Ascension clock and how is one (mounted on a telescope) used in practice?

I'm asking for more than a one-liner comment. If I had a RA value that I wanted to point the telescope at, what steps would I have to execute to get it pointed there? Do I use a second real-time clock as well, or is the RA clock the only timepiece I need? Is it a timepiece, or is it an indicator of the telescope's position? Do I do simple subtraction? Do I also need to read something else out from the telescope separately?

How exactly would this have worked in practice back when the "clock" was first installed on this historic telescope?

above: cropped and annotated, from here Credit: Fox News

below: screen shot from Restoring Lowell Observatory's Clark Refractor (mentioned here) cropped, rotated, enlarged, sharpened.


texts: What would change if Venus rotated at a speed and direction similar to Earth?

texts:
I am interested in two aspects of this question. Imagine that Venus had a similar rotation speed and the same direction of rotation that we have here on Earth.

What would change for Venus itself? I'm interested about changes in the core and mantle behaviour, a potential magnetosphere, changes in the atmosphere and tectonic plates.

What would be different for the other planets near the Sun? I'm interested about changes in gravitational resonance and potential orbit changes.


texts: Is there a pattern between the mass of a body and the mass of orbiting objects around it?

texts:
I was looking at Wikipedia's Solar system page, and it says that Sun represents 99.86% of the whole solar system mass. I found that pretty huge.

So i calculated ratio of masses : Earth / (Earth + Moon) and it's about 98.78%.

I did the same with Jupiter : Jupiter / (Jupiter + Io + Europa + Ganymede + Callisto) and it's about 99.97% (I ignored small satellites).

Why is it such a high ratio in this 3 examples?
Is 1% a regular number for satellites' mass?
It is simple gravitation maths ?

I understand that one body has to be much more massive in order to be a planet-satellite system, otherwise it's a double planet system. But I would have thought 90% would be enough.


texts: Creating an HR diagram from tabulated stellar data

texts:
I teach statistics and study Astronomy.  I'd like to create an activity for my statistics students using star data.  They could enter the data into Excel and create an HR diagram.  We are currently studying Correlation & Regression.  I wanted to show them that a scatter-plot can be VERY interesting.

Where can I get stellar data that is already in a format that my students can use excel to create a scatter-plot?  Unbeknownst to them, they will create an HR diagram.


texts: How long would it take for a black hole the mass of our sun to swallow our solar system?

texts:
If a hypothetical black hole with the mass of our sun would appear in place of the sun.
How long would it take before our entire solar system (everything inside our heliosphere) to be swallowed by this black hole?


texts: How Did Early Astronomers Measure Distances?

texts:
Prior to the era of radar and other forms of radio/RF/EM ranging, what approaches, methods, and techniques did early astronomers (e.g., Kepler, Cassini, Copernicus) use to measure the distance(s) from Earth to various objects (such as: Mars, Venus, Alpha Centauri, etc.)?

Is there an especially informative article (say, Scientific American, Sky) or book that explains their efforts and results (e.g., how accurate were their computations?)?

References and citations are warmly welcomed!


texts: What is this "time travel" these popular blogs refer to?

texts:
I am getting confused by some "popular science" about time travel, such as

or "Time Travel Is Real. Here Are the People and Spacecraft Who Have Done It":

It is indeed an interesting property of physics as we know it, and a great gift from the theory of relativity. It leads to useful perspectives on the nature of time as exemplified in the Twin Paradox example: When you travel for instance at a Lorentz factor of γ = 100 (99.995% the speed of light) for 10 years, time "dilates" to thousand years. For instance it has been proven experimentally that muons would "tick" slower, and therefore for a measure of time in seconds. Similarly, I would assume that extending this property at a macroscopic scale, your whole body would slow down...

My question is to know if will you "live for a thousand years" (internet abounds of such statements as in this example forum and may be interpreted as such in the headlines above), or rather that during the 10 years of your travel (in your spaceship) and which would be measured as 1000 years in another frame of reference (the  earth), you would have aged by "only" 10 years in your spaceship - time "froze" during the travel.


texts: How do you draw the ecliptic on a celestial sphere sketch?

texts:
I don't really understand how it's drawn on sketches of the celestial sphere. At first I thought it goes through east and west, but it does not. How do you know where to draw it?

Example from Roy and Clarke, Astronomy: Principles and Practice:


texts: what would a captured planet do if it was in a retrograde orbit?

texts:
If our solar system some how captured a rogue planet, and it orbited the sun in the opposite direction to all the other planets,

what major affect would it have on the stability, would its drag cause all the other planets to slow down ?

could it be possible for it to be sustained at all ?


texts: What particularly causes the T Tauri star to eject the strong bipolar wind which clears the gases around the star?


texts: How long would a near-light-speed trip to proxima centauri take from the traveler's and the earth-observer's perspectives?

texts: Lets say the spaceship is traveling at .9c to Proxima Centauri. How long does this trip take from the observational standpoint of the passenger vs. the observer from Earth?


texts: What astronomical observations would give conclusive proof of alien life?

texts:
There are several ways we are coming closer to answering the question "is there life elsewhere in the universe?". One is by first understanding very well the origin life on our own planet. Another is by trying to look for radio signals from extraterrestrial civilizations. Another is to try to search for habitable exoplanets, and eventually examine the habitable ones in detail via direct imaging. Another is too look for evidence of life or life that existed in the past right in our own solar system (for exmaple on Mars, Titan, Europa, etc).

1) Have I missed any other astronomy-related approaches to answering this question?

2) Short of radio contact from an ET civilization, or a visit by aliens, or the discovery of life/past-life in our solar system, what would give conclusive evidence of alien life in the galaxy?

For example:

In 20 or so years when we develop the technology to directly image exoplanets, we will be able to determine their chemical composition and characterize their structure. If astronmers who study exoplanets found what they are looking for -evidence of oxygen and other biomarker gases - this might be highly suggestive of life, but not conclusive evidence. What kinds of observations of an exoplanets could enable us to say with ceartainty "there is life on this planet"? Short of telescopic observations of truly unbelievable detail, I cannot think of a way that we can look at a planet and say "yes there is life on it, or no there is not" other than perhaps if seeing lights on the dark side of the planet.

Edit: Actually, I forgot the obvious scenario where there are trees/grass on the exoplanet.  But I don't think the plant life is required to be a different color from the rest of the terrain, and a planet with aliens does not have to have plant life. So we might not be able to detect life visually.


texts:
It seems everyone is on the same page about there being no "absolute velocity" due to the fact that everything is relativistic. However, this leaves me confused. This seems to be disconnected with the concept that the speed of light is in fact an unchanging constant. But to state that all speed is relative to an object is to essentially say, "speed does not exist, but is only relative to an observer". But yet, the speed of light is a calculable constant that never changes. How then, can we say, there is no such thing as absolute speed?

If I throw a flashlight in space that is turned on 50mph, does the speed of the emitted light from the flashlight increase by 50 miles per hour in the direction I threw it? Of course not. We know this. But if this is truly the case, how then can there not be an absolute velocity which could be calculated by determining the speed of light in relevance to the object we're measuring (since the speed of light is constant)?

Please help because this is bothering me.


texts: How do astronomers at SETI know if they received intelligent radio signals from other planets?

texts: Do they expect to see wave modulations like the ones we use in our technology? what do they expect the waves to be like exactly?


texts: If water vapor is always blown away into space, how is it able to create chemical compounds on Venus?

texts:
This is the follow-up of this chem.SE question.

According to Wikipedia, water vapor on Venus is present in trace amount (20 ppm). There are multiple reasons why Venus has very low water content:

The rich carbon dioxide atmosphere generates the strongest runaway greenhouse effect in the Solar System reaching temperatures at least 735 K, hot enough to boil most of the water vapors.
Free hydrogen and oxygen atoms  has been swept into interplanetary
space by the solar wind because of the lack of a planetary magnetic
field
Water vapors are continuously blown away by the solar wind through the induced magnetotail.
UV and photodissociation of water vapor creating hydrogen and oxygen atoms and radicals
High D/H ratio in Venus due to hydrogen atoms escaping into space since it is light thus unable to form water
The atmosphere is rich in sulfuric acid clouds which is a powerful dehydrating agents. Most of the water reacts with H2SO4 to form hydronium (H3O+) and bisulfate (HSO4-) ions. As a result, the concentrations of “free” H2O in the acid solution and in the vapor over the acid are extremely low.

So, the question is "since water vapor is always blown away or reacting in some way and there is only a trace amount of stationery and unreacted water vapor available, why/how is it able to create chemical compounds like phosphoric acid and sulfuric acid?"

Background information
A 1986 paper1 concluded that P4O6 is the main phosphorus bearing gas on Venus from the Vega mission results. It was also reported that some phosphorus bearing particles were present which was found to be phosphoric acid, H3PO4.
I am pretty sure phosphoric acid/phosphorous acid is the result of reaction between phosphorous anhydride and water vapor in sulfuric acid environment (which is later speculated to be the pathway of phosphine formation). But "is water vapor present on Venus sufficient enough to form phosphoric acid? What is the concentration of phosphoric acid on Venusian atmosphere (which would later contribute to formation of phosphine)?"
Reference

Krasnopol'skii, V A. Vega Mission results and chemical composition of Venusian clouds. United States: N. p., 1989. Web. doi:10.1016/0019-1035(89)90168-1.
https://www.vanderbilt.edu/AnS/physics/astrocourses/AST101/readings/water_on_venus.html


texts: Beamsize in radio/microwave observations

texts:
In radio/microwave observations, I understand the beamsize is the response of the telescope to a point source - effectively, the telescope's resolution.

Now, the Planck satellite (par exemple) combines different frequency channels in a variance-weighted map. These different channels in general will have different sensitivities, and different beamsizes.

Suppose you coadd two (or any number really) of these channels. What will be the effective resolution of the resulting map?
For instance, suppose we take channel 1 with a 5 arcminute beamsize (FWHM), and channel 2 with a 12 arcminute beamsize (and let's suppose they have the same sensitivity).
What will be the resolution of the inverse-variance weighted map? How will this change if the sensitivities differ?


texts: Bunch of stars moving on sky in triangular and different other shapes

texts:
Today I saw different Stars are moving on the sky in shapes of triangle and some randomly. its about 4:20 am in Nasarpur Pakistan and last star I saw at 4:32 am. They are moving in direction (North 345) degrees. Any one told me what is it?

I also saw some stars moving in other direction and they are very bright. I observed them they are near to earth w.r.t to other non moving stars ?


texts:
The unique characteristics of Be stars are mainly because of their circumstellar discs.
I wonder what makes Be stars special that only they have unique characteristics?
Which kind of stars have discs generally?
Why are there no Oe and Ae stars?


texts: Centre of the singularity that is the big bang

texts: If it's true that the deeper we look into space the further back in time the light is coming from then does that mean that just behind the cosmic background radiation the entire sky is filled with an unviewable image of the singularity that was the big bang and can that mean that we are sat at the centre of the Big Bang?


texts: Can an amateur astronomer bounce a laser off the moon?

texts:
In the TV show "Big Bang Theory" episode "The Lunar Excitation", the gang fires a laser from their rooftop, bounces it off mirrors on the moon, and measures the laser coming back on a computer.

Is this really possible?

I know scientists have successfully done this, because it's why NASA put the mirrors on the moon.

Wouldn't this require very precise targeting by the laser to hit the mirrors?

My question is, is it possible for an amateur to successfully perform this experiment?


texts: In the two body problem, if each body is given an initial condition as a momentum vector, what is the transient part of the solution as it settles into the steady state orbit?


texts:
I know the title sounds odd.  You might be thinking "Doesn't Mercury have the highest uncompressed density of any terrestrial planet?  Much higher than a planet its size normally should have?" Here's the thing, though: Iron has an uncompressed density of $7.874\ \mathrm{g/cm^3}$ and silicon has an uncompressed density of $2.329\ \mathrm{g/cm^3}$. I know the distinction for planet composition is usually metals-silicates, not iron-silicon, but iron and silicon comprise the vast majority of those two categories.
Mercury is said to be 70% metals 30% silicates with an uncompressed density of $5.4\ \mathrm{g/cm^3}$.1 However, if you run the numbers, 70 % iron and 30 % silicon gives you an uncompressed density of $6.21\ \mathrm{g/cm^3}$, or over $0.8\ \mathrm{g/cm^3}$ higher. My question is, why is Mercury's actual density lower than my proposed figure? I know that there are other materials in Mercury, like nickel, sulfur, etc., but can these things really make up the difference?

1Wikipedia and NASA


texts: What is the force of a CME on objects in space?

texts: I've been reading a little bit about coronal mass ejections lately and they seem really interesting, and they cause a lot of amazing things to happen. However, one thing I haven't seen is the physical force they can have on objects. CMEs seem to have a lot of mass and they're moving at a high rate of speed so I imagine they must have some effect on objects in space, right? What kind of effect can they have on smaller objects like meteoroids, comets, or satellites (as far as orbit, rotation, anything else)?


texts: To several decimal places, how many days are in one year?

texts:
This morning I was interested in finding out how many days are in one year on average, to several decimal places (because I am a mathematician, so I like to be accurate). Unfortunately, Googling the phrase "days in a year" results in several answers that differ as soon as the third decimal place (taking into account rounding).

A second question in addition to the title question: Does the duration of earth's orbit increase and decrease, or change only monotonically over time?


texts: What determines the configuration of orbits in a binary system?

texts:
There are essentially two configurations of orbits a system with two bodies can have:

A configuration where the paths do not cross:

A configuation where the paths cross:

Note: Size of the bodies relative to one another is unimportant here.

What determines which of the two configurations a binary system will develop into?


texts: What is the extent of the "worldwide campaign" to observe near-earth object 2012 TC4?

texts:
This nifty answer describes and provides links to the data of the recovery of near earth object 2012 TC4, and the answer also shows the first actual image of the body for this pass. At apparent magnitude +27 (at about 52 million km) it may be the faintest asteroid to have been imaged to date. It's worth visiting that answer first before reading on here.

This comment points out that 2012 TC4 appears on the Goldstone Asteroid Schedule, a list of upcoming planned observations of asteroids by antennas at the Deep Space Network. Here are the entries for 2012 TC4 in the Upcoming Observations and Past Observations tables:

Upcoming Goldstone Observations
DATES           TARGET    H     Notes:
2017 Oct  9-14  2012 TC4  26.7  Close approach = 7.9 Earth radii on Oct. 12. NHATS

Past Goldstone Observations
DATES           TARGET          Notes:
2012 Oct        2012 TC4        Echoes not detected. Likely equipment issues.

I noticed at the top of the page there is a link to the The Arecibo asteroid radar schedule, and in the fifth line of the list shown in the screen shot below, I see that for 2012 TC4 there will be what is labeled there as a "WORLDWIDE CAMPAIGN!" of observations. The all-caps and exclamation point are a direct quote from Arecibo's table.

Question: What is the extent of the worldwide campaign to observe 2012 TC4? How many facilities? Is it coordinated? Perhaps simultaneous reception of reflected signals by multiple sites? Will it be coordinated with other observations such as infrared or optical wavelengths?

The plot below the Arecibo table is made from JPL Horizons data in the Earth-Moon barycenter frame. It shows +/- 24 hours from closest approach.
The hyperbola (red) is the calculated trajectory of 2012 TC4 with dots every 2 hours and the short, (roughly) circular arc is the Moon, as descried in this question. The closest approach to Earth's center is projected to be about 51,000 km. These are preliminary calculations based on the first observation and may be refined a bit as the time of closest approach nears.


texts: Conflicting information about the star Delta Pavonis?

texts: Delta Pavonis has about the same mass as the sun so I would think that the evolutionary path would be about the same (the mass is given as O.991 M(Sun)/ not sure how we get this so accurately). It has been estimated to be about 6.6 to 6.9 Ga with a luminosity of 1.22 L(Sun). This all makes sense if you put it on the main sequence where we will be in a couple of billion years (after T(max) in about a billion years). The problem is that the surface temperature is only 5550K (spectral) and for this reason is thought to be in subgiant phase which isn't supposed to happen to us for about another 5.5 billion years. Delta Pav also has a very high metallicity [Fe/H] of +0.33 which also screams "subgiant". What am I missing?? (data from Wikipedia sources)


texts: Space telescope located in outer solar system

texts:
I want to pose a question from someone who's astronomy knowledge would fit neatly onto a single piece of paper so please bear this in mind with any comments or answers. I am interested and want to learn. I could not find a sane answer to this via a search engine.

The question: If in theory we placed another Hubble telescope (or similar instrument of at least equal or ideally more power) either on or very near the dwarf Pluto, as in in its orbit if we did not consider a ground mounted instrument, what if anything would or could we gain in astronomical knowledge ?

I do realise data transmission from such a distance would take time, power could be a concern and the fact if anything went wrong it would be beyond any sensible help, not to mention logistics in getting it there in the first place.

I also realise this is a completely hypothetical question too but I am genuinely curious if we would "see more" (so to speak) with such an instrument so far out.


texts: Does Earth's magnetic field become stronger when a solar flare hits?

texts:
This curiosity arises as follows: when ejecta from a strong solar flare hits Earth, will the Earth somehow counter its impact with a stronger magnetic field.

Or, earth's magnetic field as limited power strength to resist?


texts: Why is Chandrasekar Limit expressed relative to Sun?

texts:
In 1931, Chandrasekhar was able to show that there is a certain critical mass (Chandrasekhar's limit) beyond which a white dwarf cannot exist, since the electronic fluid at that point cannot support its weight no matter how compressed it is.

The core of such a star will simply collapse inward.

The critical mass, Chandrasekhar showed, is 1.4 times that of the Sun.

When I first heard this, I was totally confused. Sun is a star too. The Sun will eventually enter the Red Giant Phase, and then it will eventually become a white-dwarf.

How and why did Chandrasekar express his limit relative to Sun?


texts: Do stars come on like LEDs or wick lamps?

texts: Is stellar ignition an instantaneous thing - before, dark, after, shining brightly - or more of a process over time? In fusion research 'ignition' appears to be an event, but maybe in a protostar it starts locally and then spreads?


texts: What radio frequency ranges are most beneficial for astronomy?

texts:
I cannot get the idea of citizen radio astronomy out of my head, and choosing an antenna (design) heavily depends on the desired frequency range.
The Arecibo telescope as my gold standard operated 300 MHz to 10 GHz. Jovian Whistlers as nice solar source are observable at around 20 MHz. Then, there also some frequency bands which are commercially not used for the sake of astronomy, as depicted e.g. in a presentation:

I am now trying to figure out which frequency bands are important for astronomy for which purposes. My dream answer would contain a table with columns frequency range, benefits for astronomy, complications (like terrestrial use of the frequencies), and other remarks.
Related

Jupiter FM - What are practical and inexpensive ways for the amateur detection of signals from Jupiter, especially of the transit of her moons?


texts:
I am excited to see the 2017 eclipse in South Carolina and would like to understand where exactly the eclipse-path intersects I-95, so that I can plan a day-trip.

I have approximated at roughly Santee,SC, but would really like to overlay and pinpoint the eclipse-path intersection with I-95 in Google maps (blue line in .kml file).  Unfortunately, the KML file does not show I-95

Hasn't someone already done this with the web version with Google maps?
Is there a simple process to either embed I-95 in the Google Earth .kml or
Command Google Earth to overlay the blue eclipse path over the internet connected map data?

I was able to plot Santee, SC (on I-95) on the .kml file:

Any edits to sharpen or clarify questions are appreciated.  I pose this question to the astronomy community because I think that someone has already done this.  See you at the eclipse!


texts: Light brightened dimmed disappeared reappeared

texts:
My son and I saw an unusual light sit in one spot for 15-20 minutes as it got very bright and dimmed, got bright, disappeared and reappeared repeatedly.
It then slowly moved north-west then finally headed west and completely disappeared. it was 45 minutes from the time we first seen it to when it disappeared. I've been searching the web since but couldn't find anything that matches the description of what I saw.
This was March 16th 2020 about 10pm.


texts: Using setting circle for Right Ascension

texts:
I'm a little bit confused about the setting circle of my EQ5 mount. Basically, I'm trying to find M42 nebula using Sirius star as reference. So, considere that I did the following steps:

A) Polar aligned for south pole
B) Pointed the telescope to Sirius star
C) Adjusted the RA wheel to 6h45m and DEC wheel to -16º42'

Now, I want to view the M42 nebula basing only in the RA and DEC wheels (without using the finderscope or whatever).

Then, I did:

D) Changed the coordinates in the EQ5 mount to match RA 5h35m and DEC -5º23
E) Spent 5 minutes performing the step above (D)
F) Looked in the eyepiece

So my questions are:

1) After doing all these steps above, will the M42 nebula be 5 minutes away from the center of my eyepiece? So instead of using RA 5h35m I will need to use RA 5h40m?(??)

2) If yes, will I need to perform all the above steps every time that I want to see a new object? I mean, as fast as I can, to minimize the RA error...

3) And if the answer is yes again to Question (2), how useful is the setting circle under these conditions for you?

I will appreciate any kind of help.

[]s


texts:
I just looked at the sky and saw a star, not so bright but moving very fast and in almost a minute it disappeared, as it was so fast.
Timing was in between 9.35-9.45 PM in Nuremberg, Germany.
My location is 49.45, 11.06.

So was it International Space station?

Anyway, I'm going to verify it after 92 minutes if i am able see it again.


texts: How far should the source be, for the gravitation waves to be visible on Earth?

texts:
If I understand it well enough, gravitational waves cause ripples in the space-time fabric. To our eyes, that would look like those rippling-effects on amateur videos.

Where does a source have to be, in order for the effects of gravitational waves to be visible, here, on Earth.


texts: Is Barnard 68 the only cloud so close to us that there are no stars between us and it?

texts:
Regarding molecular clouds / absorption nebulae / Bok globules / obscuring clouds,

(I'm not sure if there's one generic term encompassing all those and any similar obscuring clouds - I just used "cloud" in the question title),

is Barnard 68 the only one so close to us that there are no stars between us and it?

If not, what is the list of such?  (Are we observationally confident about this, at this stage?)

I guess a related question would be: "about what is the density of bok globules near us?" ... in a cube of 1000pc on a side, about how many bok globules are we talking? One or two or thousands??

http://sci.esa.int/gaia/60207-barnard-68/


texts: Current best-known Drake Equation values?

texts:
Frank Drake's equation is used to estimate $N$ the number of civilizations we might be able to communicate with in our galaxy:
$$N = R_\star f_p n_e f_l f_i f_c L$$
where:
$R_\star$ is the average rate of star formation in the galaxy
$f_p$ is the fraction of stars with planets
$n_e$ is the average number of goldilocks planets per planetary system
$f_l$ is the fraction of goldilocks planets that actually develop life
$f_i$ is the fraction of life bearing planets that develop intelligent life
$f_c$ is the fraction of civilizations that broadcast their existence into space
and $L$ is the length of time for which a civilization broadcasts their existence
Question
Have the many exoplanets we've discovered in the last several decades improved our estimates of $f_p$, and $n_e$?  Are these values different than what was guessed about prior to the discovery of the first exoplanets?  What is our current best estimate for $R_\star$ for the Milky Way?


texts: Green objects in Hubble Ultra Deep Field

texts:
I was wondering what are the green objects that you see scattered in the Hubble Ultra Deep Field image (Warning possibly large/slow download : http://imgsrc.hubblesite.org/hu/db/images/hs-2004-07-a-full_jpg.jpg)

A crop of the image reduced in size :


texts: What is the large astronomical instrument shown in this 1918 eclipse expedition photo?

texts:
This nice video musing about (among other things) the US Naval Observatory's $3,500 expedition to Baker City or at least Baker County Oregon to observe the June 18, 1918 solar eclipse, there is a photograph of the expedition showing both normal-sized portable telescopes, and in the background a very long telescope (at least 6 meters, can't see the end) held up by a ladder, with an even longer tent extending backward from the shack sitting at the bottom of the telescope along the ground.

What is this instrument? How does it function optically, and what kind of data does it produce?

below: Screenshot from the video, photo credits available at the end.


texts: Can radio telescopes such as arecibo image the subsurface of asteroids or planets?

texts: This was done with the moon: Radio Dishes Peer Beneath Moon's Surface


texts: How much solar energy concentrates at Jupiter's focal point via gravitational lensing?


texts: Is it possible that a satellite creates a forever eclipse?

texts:
So, to add a bit of context, I’m doing the NaNoWriMo challenge, which consists of writing a novel of 50k words in one month. My whole idea is based around the following question: What would happen if the sun were to suddenly disappear?

To make it short, the story is about a colony on a faraway planet, which is settled for few generations already. And one day or let’s say, in less than a month, the sun disappear. So far, so good. Except I need a valid reason as to why the sun disappear… I have found some ideas (dust from volcanic eruption, change of orbit, dying sun, etc…) but none of them looked good enough. (I’m open for suggestion if any.)

I’m now investigating the possibility that the planet would gain a satellite big enough to hide the sun on the whole planet (like an eclipse but lasting forever). This topic lead me to think that if the satellite is in geostationary orbit, it is possible. But there is still some questions I can’t get my head around.

How fast a new satellite can “appear”?
Is it possible that a bigger but “lighter” (with less gravitational force) satellite can orbit around a smaller but “heavier” planet?
This topic reminded me that no sun means no heat. Can the geothermic activity of a planet be enough to prevent the surface from being impossible to live on? (Off topic.)

So, basically, the question is, if it's possible to have a forever eclipse, how ?

I’m sorry in advance if the questions are not clear enough, even though I understand the basics, I don’t necessarily have all the technical terms.

Thank you !!


texts: Which scenario will be worse for the ultimate fate of the Universe, forever expanding or the "Big Crunch"? Will the Universe be destroyed in both scenarios? At the present time does it appear that it will expand forever or will the expansion stop sometime in the future?


texts: How can we tell if the asteroid 2013 TV135 will hit Earth in 2032?

texts:
Some astronomers in Ukraine have estimated that there is a small likelihood (1 in 63,000) that the asteroid 2013 TV135 will strike Earth in 2032. (source)

Don Yeoman of NASA JPL says:

  with more observations, I fully expect we will be able to significantly reduce, or rule out entirely, any impact probability for the foreseeable future.

How can we improve our estimation of the potential threat posed by 2013 TV135?

That is, what process and techniques are used to calculate and increase the accuracy of our collision threat estimation?


texts: Why is sunset on 21st of June not the latest?

texts:
Why is the sunset not the latest on 21 June, but only on 27 June. Purely geometrically regarding the orbit of the two celestial bodies this should not be like this?

Is there somewhere a good source, that explains this situation ?


texts: What will the PRECISE time of the Summer Solstice 2020 be?

texts:
I'm trying to explain to my daughter that the Summer Solstice is not a day of the year, but an exact instant in time.  My search shows that this will be about 21:43 or 21:44 UTC tonight.  To make my point I searched for a more precise time.  I figured I could find a time accurate to at least the second, or hopefully several places after the decimal , but I couldn't find anything.
Can anyone show me a source for the precise time of the Solstice to at least the second?  To the millisecond?  The microsecond?


texts: Is Earth unique in its fairly clear atmosphere?

texts:
So, we have surface pictures from two alien planets, Venus (captured by the Venera 13), and Mars (captured by the rover).

Both of these pictures appear to be very dusty. For Venus we see strong storms; that makes sense. However, the Martian air also appears very dusty. Is Earth relatively unique in its clear atmosphere?

Mars

Venus

Titan (Thanks LocalFluff!)


texts: What happens when an Ultra Massive Black Hole cannibalize another?

texts: Say hypothetically an UMBH with 50 billion solar masses (supposedly upper limit) is beginning to merge with another (Super)MBH similar to Sagittarius A* that sits at the center of the Milky Way Galaxy, what would happen next in this clash of the titans?


texts:
In February, a meteor entered the Earth's atmosphere over Chelyabinsk, Russia and exploded, producing a shockwave blast that damaged hundreds of buildings around the explosion site in Russia.

But why did it explode? Why didn't it simply burn instead?


texts:
Given a date, I'd like to return the lunar phase.

Jean Meeus's Astronomical Algorithms book and the many packages like PyEphem that make use its algorithms provide ways to calculate when a primary phase (New, First Quarter, Full, and Last Quarter).  The secondary phases (Waxing Crescent, First Quarter, Waxing Gibbous, Waning Gibbous, and Waning Crescent) can be easily calculated as falling in between the primary ones.

The percent illuminated the moon (or any other body between the observer and the Sun) can also be calculated for a given point in time.

We can also calculate the subsolar point.

What isn't clear is how long the primary phases should be considered to be in play.  How are labels generally determined for these phases?

The next new moon occurs 2017/7/23 09:45:34 UTC.  When should it no longer be considered new but waxing crescent?

When it is 1.0% illuminated?
When the subsolar point moves 5 degrees west of 180E?  10 degrees?
At 2017/7/24 00:00:01 local time?
At 2017/7/24 00:00:01 UTC?

I'm inclined to use the last.  The moon is "new" for the entire UTC day 0.0% illumination falls on.  The following day it is waxing crescent and remains so until the day the first quarter falls.

Anyone know of a standard here or rule of thumb?


texts: What is exactly the "longitude of the perigee"

texts:
Some moon phase calculation algorithms (apparently derived from Duffet-Smith's book, example here) seem to use a parameter called "longitude of perigee at epoch". What exactly is this?

Can I assume this is the same as the longitude of the periapsis? Can I just calculate it adding the longitude of the ascending node and the argument of periapsis together?

Unfortunately, all the data that I find on this parameter is either related to Duffet-Smith's book or algorithms based on it. So, I have no idea on how this can be calculated for a specific epoch.


texts: Calculate Dec and RA of a star from Euler angles and GPS data

texts: I have 9DOF sensor (accelerometer, gyroscope, and magnetometer) that gives orientation via Euler angles (yaw, pitch, roll). Along with GPS data (latitude, longitude, elevation, time) this is passed to a PC application that has to calculate Dec and RA of a target (e.g. star). Sensor and GPS receiver are mounted on a telescope, so it should give the celestial coordinates of a star. The problem is that I don't know how to get Dec and RA from those data. I would very much appreciate a detail explanation of how I could get this.


texts: How deep and shaped is the depth of a black hole?

texts:
A common representation of a black hole is a black circle which if I'm correct, indicates its breadth.

This representation depicts it as a 'plate', so a really small depth compared to its breadth.

On this other representation, its depth has a funnel shape.

Question:

How deep and what shape has the depth of a black hole ?


texts: Can radio-based telescopes produce visible light images?

texts: It's a fairly simple question (at least in my layman's mind). Can a radio telescope that has no mirrors or lenses to capture visible light (to human eyes) still produce imagery like an optical telescope such as the Hubble? I'm talking just ROYGBIV light (no infrared or UV).


texts: Does a star's rotation always match a planet's orbit?

texts:
For a planet orbiting a star, is it ever possible for a star to be rotating in the opposite way on it's own axis compared to the planet that is orbiting the star?
Or do gravitational forces mean the planet will always orbit a star with the same rotational direction as the star's axis rotation ?


texts: Calculating historical star maps from proper motion

texts:
I'm working on some software which needs to calculate the position of stars and galaxies visible to the naked eye at different periods of human history.

The Yale Bright Star Catalogue gives the position and proper motion of visible stars.

Is calculating the historic positions simply a matter of multiplying each stars proper motion by the number of years between the date in question and the epoch, then subtracting the result from the position?

If so how far back in history could one go with this method and still produce a map that resembles what a human would observe with the naked eye? Would this method alone be sufficient to go back as far as 5000 years or are the other factors in play here that would need to be accounted for to make this accurate?

My criteria for "accurate" here is that a human observer wouldn't see a noticeable difference between the map and the night sky with the naked eye. Smaller inaccuracies are tolerable.


texts: What factors influence the Widmanstätten pattern in iron meteorites?

texts:
The cores of iron meteorites exhibit beautiful Widmanstätten patterns, as shown below in the Alvord meteorite (photo by Jim H):

I understand these patterns form when the molten nickel-iron core of its host body cools. As with normal crystal formation, slower cooling rates lead to longer crystal-formation times, which leads to larger crystals.
Beyond that, what factors influence the formation of the crystal, and in what ways?
I imagine composition and cooling time are the dominant factors....


texts: How can the CMB have a "monopole anisotropy"?

texts:
Wikipedia's Cosmic Microwave Background (CMBR) radiation monopole anisotropy (ℓ = 0) says

When ℓ = 0, the ${\displaystyle Y(\theta ,\varphi )}{\displaystyle Y(\theta ,\varphi )}$ term reduced to 1, and what we have left here is just the mean temperature of the CMB. This “mean” is called CMB monopole, and it is observed to have an average temperature of about Tγ = 2.7255 ± 0.0006 K with one standard deviation confidence. The accuracy of this mean temperature may be impaired by the diverse measurements done by different mapping measurements. Such measurements demand absolute temperature devices, such as the FIRAS instrument on the COBE satellite.

Question: So in this case is the use of the word "anisotropy" vestigial? It came along for the ride when higher order terms (especially dipole) were assigned meanings and implications? The monopole term is not really an anisotropy at all, is it?
It might be the case that monopole anisotropy has a well defined or accepted meaning, and that would be an interesting answer. It's hard to prove a negative though.


texts:
First of all, I'm from Syria. In Syria we have 70% of the night without electricity. So I love hanging out at this period of time in the night, looking up just as Prof. Stephen Hawking said to the sky, observing the beauty of the night sky. Tonight, when I was looking arbitrarily I saw a star. Suddenly its brightness increased gradually, and then this star released two big sparkles. They were more like distorted yellow or golden rings formed or more like waves.

I don't know how to express this phenomenon! Then those two sparkles disappeared, and the brightness of this star decreased very very fast until it just disappeared. It was the first time in my life I saw something like this! I just don't know what to say! This phenomenon lasted for a couple seconds.
I was shocked as much as you can imagine. I was unable to speak, totally impressed! I just cannot express my feeling! Maybe this is not a supernova! But what is that? Why did this star do that?


texts: How many judges sat on Galileo's trial over heliocentrism and who were they exactly?

texts:
I saw several chronologies of the trial online but most of them only mention the name of Urban 8 as involved in the actual court proceedings. How many judges were involved and who were they exactly?

Note 1. Reading the small print at wiki I found the names of the three of the ten cardinals who did not vote to convict: Francesco Barberini, Laudivio Zacchia and Gaspare Borgia.  I still don't know the names of any cardinals that voted to convict.

Note 2. Material related to the trial can be found in "Hidden agenda of the Galileo trial?" on the History of Science and Mathematics Stack Exchange site.


texts: Could binary gas giants have ring and moon systems?

texts: Would any moons/rings around either of the gas giants stay intact or get ripped apart by the tidal forces between the two giants? If any moons/rings are able to form around either of the giants, is there a limit to how large a ring system could be, or how far a moon could orbit?


texts: cosmic-microwave-background - 2.7 degrees but does the Big Bang care?

texts:
The Big Bang is a proposed answer to the beginning of the universe, and the Cosmic Microwave Background or CMB is a central part of the evidence for it.

Now suppose the measurement returned a different value than 2.7K.

What if it were 0.27K or 27K?  Would the Big Bang theory still work with a few minor adjustments or is the specific temperature of 2.7K critical evidence that the theory works?

Edit: I have removed a paragraph which was not mine asking about small changes in temperature. It is a fundamentally different question. I am more interested in how firm the evidence for the BB theory is, not its details. At least for this question.
However if uhoh who seems to have done the editing thinks it a fair question, I would certainly welcome it - in another post.


texts:
What lies near the center of the galaxy is of great interest and in recent times the motion of dozen(s) of stars at the center of our galaxy orbiting around Sgr A* have been measured in great detail. I show an example below. Though the field is only roughly 1 arc second wide, I don't see any non-orbiting background stars.

This led me to wonder...

Question: How far have stars been seen beyond the center of the Milky Way? Though this area is opaque in visible wavelengths, infrared imaging and interferometry has led to sharp images near Sgr A*. But intentionally imaged or not, how far have objects been seen beyond this distance but appearing near the center of the galaxy due to geometry? Have stars been imaged clear through the center and out into the far side of the galaxy?

Any wavelength is fine, as long as it's image-like and the answer indicates that the object lies beyond the center of the galaxy and how that could be determined.

above: homemade GIF from ESA video ESOcast 173: First Successful Test of Einstein’s General Relativity Near Supermassive Black Hole


texts: Why is there no concavity in the orbit of the moon around the Sun?

texts:
Such questions have been asked here and I have read the answers some of which are quite informative. However, I want an answer that's straightforward.

I have gone through the following paper by A B Turner titled The Moon's Orbit Around The Sun.

In this, the author concludes that the curvature of the Moon's orbit around the Sun in the new moon positions, $k_n$ is approximately 1.5 times of the Earth's orbit around the Sun, which is approximately the same as that of the Moon's orbit around the Sun in the full moon positions, $k_f$.

$k_n$$\approx 1.5k_f$, which is intuitive considering the fact that in the new moon positions, the moon experiences gravity from both the Sun and the Earth in almost the same direction.

My question is, then, how does the Moon's orbit manage to not have any concavity, no matter how minute, while transitioning from the full moon to the new moon positions? Isn't that not a mathematical impossibility?


texts:
Overview:

Taking a planet Ganymede for example (moon, technically I suppose). Ganymede is huge (well, in contrast to other bodies) and I've noticed a pattern between larger bodies and atmospheres. Usually it seems that the larger a body is, the more likely it will have an atmosphere (I know this isn't true, but it definitely seems true, with obvious exceptions). Even when playing Kerbal space program I came up on Vall expecting to be slowed due to its huge size. Big mistake, slammed into the surface. So, if size isn't the end-all-be-all of why a planet would have an atmosphere, what really causes it? Why wouldn't something like Ganymede, doubly protected by it's own magnetic field and Jupiter's field not have an atmosphere? What causes the planet to lose it once an atmosphere is created?

You can ignore my overview rambling, I suppose my one-liner focused question is:

What are the real conditions for the creation of an atmosphere/loss of an existing atmosphere?


texts: How to choose initial state vectors for a resonant orbit numerical simulation?

texts:
How do higher numbers affect orbital resonance? is a really interesting question, and I thought I would try to do a simple numerical simulation of various resonance ratios to see if some are inherently stable or inherently unstable.
I understand that numerical simulation is inexact and so it can introduce its own instabilities so attention will have to be paid to the choice of integrators and results taken with a large grain of salt.
In order to get something to happen within say a hundred or a thousand orbits the masses of the orbiting bodies have to be large enough to have a significant impact on each other1, and so the state vectors I choose to initialize the calculation will not necessarily be those of circular orbits each body neglecting the other.
Are there any guidelines or rules of thumbs for initializing resonant orbits?

1I'll assume a central force, i.e. the orbiting bodies will not affect the position of the body they orbit, and so there won't be any indirect coupling through it.
Related:

Just how "locked" are resonant-chains of exoplanets thought to be? (e.g. K2-138 and TOI-178) (currently unanswered)
Why does the exoplanetary system TOI-178 challenges current theories of planet formation?


texts: Where did the idea that tidally-locked planets have a big hurricane come from?

texts:
I've been noticing a bit of a trend in the depiction of tidally-locked habitable planets, where they are shown having a huge hurricane-like storm over the daylight hemisphere. Here's an example, and another one in the background of this Cool Worlds video.
I'm wondering where the idea that the cloud formation over the daylight hemisphere would take the form of a single rotating storm came from. It doesn't seem particularly realistic: the Coriolis effect should tend to disrupt such a storm as it would lead to opposite rotation directions in the northern and southern hemispheres. The study by Yan & Yang (2020) "Hurricanes on Tidally Locked Terrestrial Planets: Fixed SST Experiments" predicts storms similar in scale to the hurricanes on our own planet, and the overall circulation (figure 3) appears to have separate vortices north and south of the equator rather than the single giant circulation in the artworks.


texts: What is the typical resolving power of the largest optical telescopes?

texts:
I'd like to estimate the typical resolving power of the largest optical telescopes.

I've calculated the theoretical resolving power of the VLA for 21 cm light, $$R=\frac{\lambda}{B}=\frac{2.1 \times 10^{-1} m}{2.7 \times 10^4 m}=1.6 ''$$

And I know that the largest optical telescopes on Earth are GTC, Keck 1 & 2, SALT, VLT, etc.

But I don't know how to calculate a typical resolving power in practice. How can I make this estimate taking into account astronomical seeing and other effects?


texts: How bright would a magically created 13.7B years ago white dwarf be now?

texts:
I assumed that the initial brightness is $1$, and at death it is $10^{-20}$ (since I can't reach 0 with exponentiation, it will be close enough to 0), and it lived $10^{15}$ years.
Then I solved an equation $x=-\frac{10^{15}}{ln(10^{-20})}$ to get the right results at $10^{15}$ years.
And lastly I made a graph: $y=e^{\frac{-x}{-\frac{10^{15}}{\ln(10^{20})}}}$, that gives me $y=10^{-20}$ at $x=10^{15}$ or a quadrillion years after its creation.
I got $y=0.999$ at $x=13.7\cdot10^{9}$ or 13.7 billion years, or now, which means the white dwarf is 0.999 the brightness it was when it was created during the big bang somehow.
Do these results make sense?


texts: How to form Copper from Calcium in a supernova explosion?

texts: What are the reasonable chain of reactions to form copper (63, 29) from ca(40, 20) during supernova explosion? And how it will happen? I do not understand the theory behind it. I thought that the reaction will end at Iron and now it does not make sense to me.


texts: Can a rogue planet neither orbit around a star nor a galaxy?

texts: As we know, rogue planets don't orbit around a star, how about galaxy? Can a rouge planet not orbit around a galaxy?


texts: Do we have to take gravitational lensing into consideration when measuring the size of exoplanets?

texts: For the method of waiting for a planet to pass in front of a star. rather than just measuring the light that is blocked do we also have to take into consideration the light that may not be coming to us because of gravitational lensing caused by the planet? Is the mass of a planet large enough to cause gravitational lensing significant enough for us to see an effect?


texts:
When Kepler went to Tycho Brahe, he learned that Tycho Brahe was using the mean position of the sun to note down the position of Mars. Well, Kepler needed to convert these datas of Brahe to do his own calculations for the orbit of Mars.

In this link, the difference between the real and mean position is shown.
http://www.keplersdiscovery.com/MeanSun.html
http://www.keplersdiscovery.com/CorrectedTable.html

But how did Kepler calculate the real position of the Sun? I don't get it. And due to my first language is not English it might be possible that I didn't understand some important aspects of the given links.


texts: I came across several papers (e.g. Looking for outflow and infall signatures in high mass star forming regions P. D. Klaassen, L. Testi and H. Beuther, 2011) talking about infall signatures in star formation. Can you please explain the physical meaning of it?


texts: How often are supernovas visible by the naked eye from Earth?

texts:
I heard about the 1054 supernova that was visible with the naked eye.

Of course, these events happen at random. But just like with radioactive decay, it must be possible to determine statistics on these kinds of events.
Wikipedia says

  The total supernova rate in our galaxy is estimated to be between 2 and 12 per century

but this doesn't indicate anything about their visibility from Earth. In fact, quite a few supernovas in the Milky Way probably go unnoticed, so the rate of visible supernovas is likely lower.

In addition, type Ia supernovas can outshine the galaxy they are in, so if one occurred in Andromeda or a Magellanic Cloud, it might be visible. So there possibly could be more visible supernovas than there are supernovas in just our Galaxy.

What is the average time between two supernovas that are visible with the naked eye?


texts: What is the mean distance of M53 Nucleus' stars ? (and other Globular Clusters)

texts:
Background: This Instagram post (from astronomypicturesdaily) tells that:

If our Sun were part of this star cluster, the night sky would glow like a jewel box of bright stars.

I opened this question because I've always wondered how days and nights would look like if we were part of a Globular Cluster.
I looked on Simbad and found this article named "Globular cluster number density profiles using Gaia DR2" (de Boer et al., 2019) on which number density radial profiles are derived from several clusters using DR2 data.

I guess, as a first approach, that this would depend on wether we're part of the "central region" of the Globular Cluster or, instead, closer to the boundaries. Anyways, in the first case (only because I think it's more interesting) I'd like to share some questions:

What would be the mean distance between M53's stars over a certain region? How should it be computed?
Under the assumption of being inside such a system, What would be the expected distance between us (Solar System) and neighbor stars?
Considering brightness of this stars, how would night and day sky would really look?
Is there any known exoplanet system that lies inside a Globular Cluster?
Do you think that the same question can be applied to Elliptical Galaxies?


texts: What is the meaning of ellipticity of a galaxy being more than 1?

texts:
I was recently doing a project on calculating ellipticities of galaxies using SDSS data. I downloaded the stokes parameter values (q and u) from data

$e  = 1 - \frac{b}{a} = 1 - \frac{1 - \sqrt{Q^2 + U^2}}{1 + \sqrt{Q^2 + U^2}} $
 and for few values of stokes parameters, the value of ellipticity goes above 1.

What could this possibly mean? Could this mean the data of random galaxies I've taken has irregular agalaxies in it and that's the reason for ellipticity being greater than 1? I would like to hear your opinions and answers.


texts: If the Galactic Coordinate System is made up of two values, angles of longitude and latitude, how is distance measured? If you have those two values, you get a line from the sun in a certain direction. There might be multiple objects on that line, how can you specify one of them in the coordinate?


texts: Is Ceres in the inner solar system or outer solar system?

texts: Do we consider the dwarf planet Ceres to be in the inner solar system or outer solar system (or possibly neither / in between).  It is located within the asteroid belt, but is the asteroid belt part of the inner or outer solar system?


texts: My idea of the matter is: hot stellar systems are which form of objects which have a velocity standard deviation comparable to their mean velocity. Is this correct? If it is, is there a $\frac{\sigma_v}{<v>}$ boundary, which draws a line between hot and cold stellar systems?


texts: Basic explanation of baryon acoustic oscillations; what if anything is actually oscillating?

texts:
Sci-News' Sloan Digital Sky Survey Collaboration Releases New 3D Map of Universe links to the two videos

The eBOSS 3D map of the Universe
SDSS releases largest 3D map of the universe ever created

and says

The team’s results will be published in a series of 20 papers in the Monthly Notices of the Royal Astronomical Society.

After 01:30 in the second video Jiamin Hou from the Max Planck Institute for Extraterrestrial Physics says:

However the red shift has an additional component that is due to the galaxy’s own velocity, and which moves in response to the gravitational attraction of the surrounding matter, and these two components can not be separated from each other. But the statistical analysis of the eBOSS allows us to distinguish the effects of velocity from that of expansion.

I've also looked at:

Wikipedia: Baryon_acoustic_oscillations; Cosmic sound
SDSS.org's surveys; eBOSS

but I can't get a grasp of what the term "baryon acoustic oscillations" really means.
Question: Is it possible to write or quote a basic explanation of what these are? For example, does oscillation mean there are things moving back and forth due to some restoring force? Is there something analogous to a "sound wave" out there somewhere? Or is there just a plot of something that shows a wiggly line that goes up and down?


texts: Are there any to-scale diagrams of the TRAPPIST-1 system?

texts:
Recommended to cross-post from SpaceEx: https://space.stackexchange.com/questions/38397/are-there-any-to-scale-diagrams-of-the-trappist-1-system

I was recently told that the planets in TRAPPIST-1 are close enough together that you can see them from each other, as visible, discernible planets "hanging in the sky". i.e. much like the moon.

This assertion is compatible with this question: How many things are wrong in this "artist view" of the TRAPPIST-1 system?

I'm trying to understand the implications of the claim, and started by trying to find a to-scale astronomic diagram of some, or all, of the TRAPPIST-1 system, showing the star, the planets, their sizes and orbits, to scale.

Obviously such a diagram of the (Sol-Terra) Solar System would be completely useless - a few pixels in the centre, surrounded by a 8 other single-pixel-dots around the diagram.

But if the claim is true for TRAPPIST-1, then I would expect such a diagram to be actually "usable".

But I couldn't find such a diagram. Does one exist?


texts: How do black holes form from stars that go supernova

texts: I know that the cores of stars with more than 20 times the mass of the Sun collapse into black holes at the end of the star’s life. However, as far as my understanding goes, stars with cores that become black holes can explode in a supernova. This doesn’t make sense as in order for that event to happen, a star needs to be torn apart by a shockwave created from core bounce. How can this happen for stars more than 20 time the mass of the Sun?


texts: How far above the Earth's surface does interplanetary space begin?

texts: The Kármán line is often cited as the beginning of outer space.  The Voyager probes have identified the boundary between the heliosphere and interstellar space.  Is there a agreed upon definition of the boundary of interplanetary space?  Is it the Earth's magnetopause?


texts: Why do "they" portray colliding black holes like that?

texts:
When I see an animation of two colliding black holes anywhere, it looks like two merging beads of water. But why would the event horizon form a bridge during collision? There is no material flowing in-between. Wouldn't the event horizons "push" each-other away as they merge?(the effect not the black hole itself) For what I understand the gravity would poorly, but surely, be canceled out. Wouldn't this "push" only disappear from view as they got significantly closer, where it still exists but is trapped in a much larger one?

Just to make sure, as I see the similar questions: I don't mean what happens as they collide, but rather why isn't this portrayed if it does this effect at all?


texts: Are ascending node of sun, the point of intersection of prime meridian and equator and center of earth all collinear?

texts:
I did a bit of googling but couldn't find the exact answer, so are the following 3 points collinear or not ?

1_center of earth

2_ascending(or descending) node of sun

3_point of intersection of prime meridian and equator(point of zero longitude on equator).


texts: What is the magnification of my new telescope?

texts:
I just bought a Skywatcher telescope with a diameter of 60 mm and a focal length of 900 mm. I have a 2x Barlow lens and two eyepieces with focal lengths of 10 mm and 20 mm.
How can I calculate the magnification of my telescope, for example using the 2x Barlow and the 20mm eyepiece?
I'm fascinated by watching the sky and I can't wait to try it... Unfortunately, it's currently cloudy.
One more question; what I can see to be fascinated with this telescope?


texts: How to calculate the ground track of the Moon's position on the Earth's surface?

texts:
I would like to project the Moon's position on to the surface of the Earth, starting with its position expressed as Right Ascension in degrees.

I know that the declination of the Moon corresponds to the terrestrial latitude but how can I "convert" the right ascension of the moon to find my longitude?

I'm not an astronomer, so I'm hoping for a fairly simple answer.

EDIT

My friend used this formula a long time ago:

For the time at which I want to calculate the longitude,

time_hrs = hours + minutes / 60

then using right ascension of Sun,

delta_x = time_hrs * 15 + right_ascension_sun - 180;

The coordinates of the Moon's ground track at this time are then:

longitude = Right_ascension_moon - delta_x;
latitude  = Declination_of_moon

but i don't know if is correct, or how precise it will be.


texts: Claim that 30-m class telescopes will have resolution far superior to Hubble: true?

texts:
This article makes the claim that the Giant Magellan Telescope (GMT, number 4 in the list) will have resolution 10 times better than that of Hubble, while the Thirty Meter Telescope (TMT, number 3 in the list) will have resolution 12 times better than that of Hubble.  These are claims I find impossible to believe.

A simple application of, for instance, the Raleigh Criterion ($\theta = 1.22~\lambda/D$), where $\theta$ is the angular resolution of the telescope, $\lambda$ is the wavelength of the light in question, and $D$ is the diameter of the telescope, would show that a comparison between angular resolutions is as simple as comparing the diameters of the telescope apertures.  Hubble's mirror is 2.4 m; comparing with the 24.5 m GMT and the 30 m TMT we see that the GMT will have 10.2 times the angular resolution of Hubble, while the TMT will have 12.5 times the angular resolution of Hubble.  I think a calculation similar to the one I have described is how the article linked above came up with the numbers they did about the angular resolution of these telescopes compared to Hubble.

However, the Raleigh criterion only applies to telescopes working at their diffraction limit.  Space telescopes (if they're designed well and built correctly) can work close to the diffraction limit (maybe even at the diffraction limit).  Ground-based telescopes, however, are limited in angular resolution by the atmosphere, which at best will limit resolution to about an arc-second at the best sites on Earth. Thus the GMT and TMT by themselves will not have better image resolution than Hubble.

My question, then, is whether this article is correct (possibly because of one of the reasons I list below) or whether it seems this article naively applied the Raleigh Criterion for angular resolution with no thought about how the atmosphere will affect the resolving capabilities of these large ground-based telescopes.

Possible reasons the article may still be correct:

Adaptive optics, a developing technology which can allow telescopes to correct for distortions to the image produced by the atmosphere.  Perhaps GMT and TMT will have very fancy adaptive optics systems.
Another technique, such as speckle imaging or lucky imaging.
Article could be referring to spectral resolution, rather than angular resolution (or image resolution).  However, obtaining good spectral resolution is as much the job of the spectral instrument as it is of the telescope so I don't consider "spectral resolution" to be an inherent property of a telescope.


texts: The definition of eclipsing binary star systems

texts:
In the second minimum (the 3rd step) there is a smaller decrease in light intensity. For this to happen, wouldn't you need to be looking at the plane of orbit from above rather than directly along the plane of orbit? Because if a person was looking directly along the plane, then it would just be a full eclipse of the star behind in step 3?
But then if a person is not directly looking along the plane but just sees the plane from above, doesn't this mean the definition of eclipsing binaries is wrong? The definition is 'when the plane of orbit of stars is in the line of sight from the Earth'. By 'line of sight' I assumed it meant a person from Earth is able to look directly along the plane. So was my assumption wrong?


texts:
I'm trying to understand orbital inclination by looking at the planetary orbit inclination table on https://en.wikipedia.org/wiki/Orbital_inclination (there are orbital inclinations for terrestrial and gas giant planets listed there).

By inclinations to ecliptic or Sun's equator, it looks like the Earth is the most (or least) inclined from all the listed objects having the smallest (or biggest) inclination value. However, the inclination to invariable plane seems to be bigger for some planets than for the Earth, and smaller for others.

At first, I thought that displaying the absolute value (dropping the minus sign) in case of a negative angle is the case. But if those three columns were just three different reference planes, the relative difference between planet inclinations should at least be the same in all cases. But it's not the case as, for example, Mercury's and Venus' orbital planes have 3.62° between themselves as per the inclination to ecliptic, but they have 0.48° as per the inclination to the Sun's equator.

So, how should one read those numbers?


texts: Relation between photometric redshift in a given bin and conditional probability

texts:
I take over an old question that is not yet clear for me. Indeed, I would like to formulate the equation (1) below under the form of "conditional probability" but I can't manage to do that. So I decided to ask for the question again since i think I can reformulate this relation with this conditional probalbility, and moreover since I have enough (for the instant I hope) score to launch a bounty if necessary (in case if my question wouldn't have enough attention for most of you).
In the context of photometric probe of surveys (like LSST), I need to understand the relation I have to use for photometric bins.
Considering $p_{ph}(z_p|z)$ the  probability to  measure a photometric redshift equal to $z_p$ knowing the real redshift is $z$ and given $n(z)$ the density distribution of objects, I have the following formula which gives the density $n_i$ of galaxies into $i$-th bin and that I would like to understand :
$$
n_{i}(z)=\frac{\int_{z_{i}^{-}}^{z_{i}^{+}} \mathrm{d} z_{\mathrm{p}}\,n(z)\,p_{\mathrm{ph}}(z_{\mathrm{p}} | z)}{\int_{z_{min}}^{z_{max}} \int_{z_{i}^{-}}^{z_{i}^{+}}\,\mathrm{d} z \,\mathrm{d} z_{\mathrm{p}} \,n(z) \,p_{\mathrm{ph}}(z_{\mathrm{p}} | z)}
\quad(1)$$
with $\left(z_{i}^{-}, z_{i}^{+}\right)$ which are the values of both sides (+ and -) of redshift $i$ bin.
I wonder if I can express this relation with the equivalent of Bayes theorem but with density functions (called conditional density), like this :
$$g\left(x | y_{0}\right)=\frac{f\left(x, y_{0}\right)}{\int f\left(t, y_{0}\right) \mathrm{d} t}\quad(2)$$
Or maybe by making appear the conditional probability (it depends if $X$/$Y$ are discrete/continuous, i.e (from https://en.wikipedia.org/wiki/Bayes%27_theorem#Random_variables) :
Simple form $[$
If $X$ is continuous and $Y$ is discrete,
$$
f_{X \mid Y=y}(x)=\frac{P(Y=y \mid X=x) f_{X}(x)}{P(Y=y)}
$$
where each $f$ is a density function.
If $X$ is discrete and $Y$ is continuous,
$$
P(X=x \mid Y=y)=\frac{f_{Y \mid X=x}(y) P(X=x)}{f_{Y}(y)}
$$
If both $X$ and $Y$ are continuous,
$$
f_{X \mid Y=y}(x)=\frac{f_{Y \mid X=x}(y) f_{X}(x)}{f_{Y}(y)}
$$
EDIT:  I would like to better understand the eq. (1) and in the same time to be able to interpret it as a "Bayesian" formulation knowing z_p seems to be a discret variable (I am not really sure of that since we integrate over dz_pin bottom) and z a continuous variable
Any help is welcome.


texts:
I'm trying to develop a planetarium using Tycho 2 catalogue.

To read it I use the WCSTools. But I have a problem.

On Wikipedia I have found that Rigel star has RA: 05h 14min 32,3s and Dec: -08º 12’ 06’’. I have translate them to decimal degrees (78.6375, -8.2017). I've used that to find it on Tycho 2 catalogue (file catalog.dat) but I can't find it.

To search into the catalogue I have used the function TY2READ from ty2read.c file.

And this is how I search the star:

void ReadTy2Catalog()
{
    double raCenter = 84.5;
    double decCenter = -1.2;
    double raDistance = 10.;
    double decDistance = 10.;

    int nMaxStars = 20000;

    char* filePath = "D:\\Fuentes\\Repos\\Planetarium\\StarsCataloguesLib\\Resources\\";
    Ty2Read read;

    read.Read(
        filePath,
        TYCHO2,         /* Catalog code from wcscat.h */
        raCenter,       /* Search center J2000 right ascension in degrees */
        decCenter,      /* Search center J2000 declination in degrees */
        raDistance,     /* Search half width in right ascension in degrees */
        decDistance,    /* Search half-width in declination in degrees */
        0,              /* Limiting separation in degrees (ignore if 0) */
        0,              /* Inner edge of annulus in degrees (ignore if 0) */
        1,              /* 1 to sort stars by distance from center */
        WCS_J2000,      /* Search coordinate system */
        2000.0,         /* Search coordinate equinox */
        0.0,            /* Proper motion epoch (0.0 for no proper motion) */
        -20.0,          /* Limiting magnitudes (none if equal) */
        30.0,           /* Limiting magnitudes (none if equal) */
        1,              /* Magnitude by which to sort (1 or 2) */
        nMaxStars,      /* Maximum number of stars to be returned */
        1);             /* Verbose*/
}

I have checked all the stars returned and none has Rigel's RA and DEC.

What am I doing wrong?


texts: Cause of ~10 minute Oscillations in Low Energy Electron Flux in Earth's Magnetosphere

texts:
I am analyzing data from an instrument that measures low energy electron flux at Geo-Stationary orbit.  There are sharp oscillations in the particle flux of 30 eV electrons occurring from about noon to 8 pm (space-craft local).  The period of this activity is relatively consistent at about one cycle every 13 minutes.  I am trying to determine if this is a natural phenomenon or systemic contamination.

EDIT:  I have added a plot of data containing the oscillations.  The Y-axis represents counts per interval and X axis is time.  The purple line represents the south-most zone and the red the north-most.  I have intentionally removed the title/legend/labels.  The oscillations are obvious in the right side of the plot.

My question is this:

Are there any natural cycles within the solar-wind or radiation belts that have a similar frequency?

A second question:

Are there evenly spaced and distinct longitudes containing higher densities of electron cycling that the space-craft might be passing through?

Any other ideas as to the cause of the oscillation are welcome.


texts: What is the direction of a comet's dust tail before and after perihelion?

texts:
I recently created a visualisation of comet ISON's orbit. However, I received a critique that the dust tail of the comet should be pointing away from the Sun after perihelion.

As far as I know, the ion tail of the comet definitely points away from the Sun as it is blown away by the solar wind.

I want to know what is the direction of the dust-tail of the comet, before and after the perihelion. Is it always trailing the path of the comet (to a fair degree of approximation) or are there other significant effects?


texts:
This answer to What (the heck) is a Hamiltonian telescope? Is this one? confirms that the telescope in the question linked there is indeed as described and that the first lens is a full 65 cm aperture lens, the second element is a full 65 cm negative meniscus back-silvered, and some corrector lenses are embedded= within a hole in the large primary lens.
Optically I can imagine that it might be possible to let the light transmit again through the primary and still compensate, and mechanically that seems more attractive than polishing a double-sided transmission lens with a hole through the center.
But apparently that's what's been done.
Question: How to make a 65 cm lens with a 20 cm hole in it for a Hamiltonian telescope? I'm thinking about issues including the following:

Is the blank cast with a hole already, or is it drilled?
If drilled, is that before the first side is polished, before one side and after the other, or after both sides?
After drilling does one need to anneal the glass again?

Glass can experience strain-induced birefringence among other things, so I am really interested in finding out how optical surface figures are applied to both sides of this lens with a big hole in it without causing optical problems within the bulk of the glass.

Image from this answer to What exactly is a Hamiltonian telescope? Is this one?


texts:
The planets in our system are most often grouped into two categories:

Terrestrial:

Mercury
Venus
Earth
Mars

Gas Giants:

Jupiter
Saturn
Uranus
Neptune

Why is it that we don't see "in-between" planets in our system - large, rocky worlds larger than Earth but with thick atmospheres somewhat similar to those of gas giants? Are they possible? Did they not occur by random chance?


texts: Are all gas planets guaranteed to produce their own magnetic field?

texts:
All gas giants in the solar systems have two things in common: abundant hydrogen gas and a magnetic field.

I'm wondering: could there be a gas planet that somehow can't produce any magnetic field on its own?

I learned there many kinds of bizarre and unfamiliar worlds from reading up terrestrial exoplanets and moons, so I thought maybe there is a unique gas planet that doesn't produce any magnetic field - or maybe the magnetic field disappeared after a while.

BTW I'm aware of hydrogen becoming metallic under a specific condition.


texts: Do comet orbits lie in the same plane as the other planets?

texts: Two typical comets that I know are Donati's and Halley's. So comets also have orbits, but are their orbits on the same plane (such as the ecliptic) as the other planets?


texts: Of the stars in the Gaia / Hipparchos catalogs, which one is the most isolated?

texts:
This is just a matter of curiosity; I was thinking about a scifi story.

By "Isolated", I mean that if for every star (or binary) we found the distance to its closest neighboring star, then which one would be the furthest from its closest neighbor?


texts:
Related to Convert coordinates between RA/dec and WGS 84 (SRID=4326).

WARNING: I'm a noob in astronomy.

After import all stars from HYG Database (http://www.astronexus.com/node/34) I noticed some missings:

1) NGC catalog seems to have other names ( maybe Gliese )

2) Some stars have catalog names when could have simple (commom) names ('Mimosa' is 'Bet Cru').

In fact, I think the HYG Database is too professional (
select count(*) from hygn where proper_name is not null gives me only 87 stars) and keep the stars names more scientific.

Is there another database like HYG Database I can try?


texts: What is the "radiation sound speed" inside an accretion column?

texts:
I was trying to read "A New Two-fluid Radiation-hydrodynamical Model for X-Ray Pulsar Accretion Columns" and its follow-up paper both by West et al. and came across a quantity called "radiation sound speed", $a_r$.

It is defined as
$$
a_{r}^{2}=\frac{\gamma_{r} P_{r}}{\rho},
$$
where $\gamma_{r}$ is the ratio of
specific heats for the radiation field, whatever that is supposed to mean, $P_{r}$ is the radiation pressure and $\rho$ the mass density.

My question now is: How can the radiation field have specific heats and a speed of sound?
I always though only compressible fluids, gases, etc.  can have that.


texts: Where to find comprehensive list of absolute magnitudes for stars of different spectral types?  I need published paper or web page with data and reference to the source.